Variac Variable Transformer

It's mainly for older amps with the paper/oil caps. A sudden voltage surge can cause older caps to short out-which can be very bad. I would worry mainly about the tube gear but if you buy a variac, use it only any solid state gear too.

By very slowly bringing the voltage up, it will allow the caps to "reform" internally and avoid costly shorts or having to replace the caps.

It's a problem with electrolytic caps. Layer of aluminum oxide that serves as isolator diminishes over time (years) without voltage and capacitor looses its voltage rating. Applying voltage and keeping voltage at lower levels (for days) will replenish layer of aluminum oxide and capacitors will be OK. Applying full voltage to unit that was in storage for many years can cause capacitor short, thermal build-up and even explosion. Capacitors have fuse (vent) to prevent it (explosion) but it's wise to to test it.